Electrical Engineering ⇒ Topic : Millmans Theorem with sinusoidal excitation

Millman's Theorem

Millman's Theorem states that in any network, if the voltage sources V₁, V₂, ..... V_n in series with internal impedances Z₁, Z₂, . . . Z_n, respectively, are in parallel, then these sources may be replaced by single voltage source V' in series with an impedance Z' as shown in Fig.(a).

                                                        figure (a)

A similar theorem can be stated for n current sources having internal admittances which can be replaced by a current source I¹ in parallel with an equivalent admittance.

                                                                          figure (b)

Millman's theorem is very convenient for determining the voltage across a set of parallel branches, where there are enough voltage sources present to preclude solution via regular series -  parallel reduction method. It doesn't require the use of simultaneous equations. However, it is limited in that it only applied to circuits which can be redrawn to fit this form. It can not be used to solve an unbalanced bridge circuit